Problem: What's the first wrong statement in the proof below that $ \triangle BCE \cong \triangle FCE$ $ \; ?$ $ \overline{BC} $ is parallel to $ \overline{DF} $. This diagram is not drawn to scale. $A$ $B$ $C$ $D$ $E$ $F$ Givens $ \angle CEF \cong \angle BAC$ $, \ $ $ \overline{CE} \cong \overline{AC}$ $, \ $ $ \angle ECF \cong \angle ACB$ $, \ $ $ \angle CEF \cong \angle BED$ $, \ $ $ \overline{CE} \cong \overline{DE}$ $, \ $ and $\ $ $ \angle ECF \cong \angle BDE$ Proof $ \triangle BCA \cong \triangle FCE$ because ASA $ \overline{BC} \cong \overline{CF}$ because corresponding parts of congruent triangles are congruent $ \triangle FCE \cong \triangle BCE$ because SSS $ \triangle FCE \cong \triangle BDE$ because ASA $ \overline{EF} \cong \overline{BE}$ because corresponding parts of congruent triangles are congruent
Answer: Try going through the proof yourself: write down the givens, and then see if they justify the next step for the reason given. Then do the same thing for the next step, and the next, until you run into something that you can't justify, or you finish the proof. $ \triangle BCE \cong \triangle FCE$ is the first wrong statement.